A cat sleeping on its back with its paws in the air may indicate that it has a high degree of trust in its owner and feels safe. This posture usually occurs when a cat feels relaxed and secure, as its belly is a vulnerable area that it doesn't typically expose to others.
Animals are naturally wary. Many mammals are covered in fur, with their bellies being the softest part and a major weakness. Cats are no exception. Normally, cats will lie down to sleep, as this hides their softest part—their belly—under their bodies to protect them from predators.
